Papers to read (mainly): Belavin, Polyakov, Zamolodchikov, "Infinite conformal symmetry in 2-dim quantum field theory" (1984); Friedan, Martinec Shenker, "Conformal invariance, supersymmetry and string theory" (1986), Dixon, Friedan, Martinec, Shenker, "Conformal field theory of orbifolds" (1987).
Books/articles (text+reference): the books on string theory by Polchinski (2 vols); Ginsparg notes "Applied conformal field theory", arXiv:hep-th/9108028; Green,Schwarz,Witten (2vols); di Francesco, Mathieu, Senechal, "Conformal field theory", etc.